Abstract. In this paper, we prove almost global existence of solutions to certain quasilinear wave equations with quadratic nonlinearities in infinite homogeneous waveguides with Neumann boundary conditions. We use a Galerkin method to expand the Laplacian of the compact base in terms of its eigenfunctions. For those terms corresponding to zero modes, we obtain decay using analogs of estimates ...

We consider stability of periodic travelling waves in the generalized reduced Ostrovsky equation with respect to co-periodic perturbations. Compared to the recent literature, we give a simple argument that proves spectral stability of all smooth periodic travelling waves independent of the nonlinearity power. The argument is based on the energy convexity and does not use coordinate transformati...

For a contravariant 4-metric which changes signature from Lorentzian to Riemannian across a spatial hypersurface, the mixed Einstein tensor is manifestly nonsingular. In Gaussian normal coordinates, the metric contains a step function and the Einstein tensor contains the Dirac delta function with support at the junction. The coefficient of the Dirac function is a linear combination of the secon...

We study reparametrization-invariant systems, mainly the relativistic particle and its D-dimensional extended object generalization d-brane. The corresponding matter Lagrangians naturally contain background interactions, like electromagnetism and gravity. For a dbrane that doesn’t alter the background fields, we define non-relativistic equations assuming integral sub-manifold embedding of the d...

In this paper the quantum hyperbolic equation formulated in [1] is applied to the study of the propagation of the initial thermal state of the Universe. It is shown that the propagation depends on the barrier height. The Planck wall potential is introduced, VP = h̄/8tP = 1.25 10 GeV where tP is a Planck time. For the barrier height V < VP the master thermal equation is the modified Klein-Gordon ...